Question: Express this quotient in scientific notation: ${\frac{4.640\times 10^{5}} {8.0\times 10^{3}}}$
Explanation: Start by collecting like terms together. $= {\frac{4.640} {8.0}} \times{\frac{10^{5}} {10^{3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.58 \times 10^{5\,-\,3}$ $= 0.58 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.58$ is the same as $5.80 \div 10$ , or $5.80 \times 10^{-1}$ $ = {5.80 \times 10^{-1}} \times 10^{2} $ $= 5.80\times 10^{1}$